It is known that, when the pulse response of communication channels is greater than the symbol duration, or when there are multiple paths, an interference between the symbols (IBS) appears.
Currently, in order to limit the degradations of the performances in multi-carrier transmission, equalisation or pre-equalisation techniques are used.
In the alternative case of multi-carrier modulations, the use of a guard interval of sufficient size makes it possible to absorb this interference and therefore to cancel out the effects thereof. Nevertheless, when the pulse response of the channel is very long, the guard interval may adopt a large size then substantially reducing the spectral efficiency of the system.
Moreover, in some systems, the actual spreading of the delays exceeds the size of the guard interval, thus considerably impairing the performance.
In order to reduce the spread of the channel delays in single-carrier systems, or in the case of multi-carrier systems to reduce the guard interval or to ensure that the pulse response is contained therein, several channel length reduction techniques have been developed and applied to the structural definition of a channel length reduction filter of the pulse response of the channel.
For example, in the document “Adaptive channel memory truncation for maximum likelihood sequence estimation” (D. Falconer and F. R. Magee, Bell System Technical Journal, vol. 52, no. 9, pp. 1541-1562, 1973) a channel length reduction method using a minimum mean square error (MMES) algorithm is proposed for reducing the channel size. More precisely, according to this technique, the coefficients of a channel length reduction filter are obtained by the conventional application of the mean square error (MSE) minimisation criterion.
Alternatively, the document “Impulse response shortening for discrete multitone tranceivers”, (J. W. Melsa, R. C. Younce and C. E. Rohrs, IEEE Trans. Communications, vol. 44, no. 12, pp. 1662-1672, 1996) proposes an MSSNR (“Maximum Shortening Signal to Noise Ratio”) method for minimising the energy outside the guard interval or maximising the energy contained in the guard interval. More precisely, this technique models the channel in two parts, one referred to as useful “hmax” as illustrated (11) in FIG. 1 and another part to be minimised “hmin” (12) using a w filter.
Conventionally, the equivalent channel is represented by the following equation:heq=h*w=(hmax+hmin)*w 
According to this method, the coefficients of the filter are obtained by maximising the energy ratio between hmax and hmin using a single optimisation criterion.
In the document “Impulse Response Shortening through Limited Time Reversed Channel in MB OFDM UWB Systems”, (S. I. Husain, J. Yuan and J. Zhang, ISCIT 2007, pp. 1269-1273, October 2007), the channel length reduction filter effects a time reversal limited to the hmin part.
Moreover, the combination of two distinct filters is also known from the prior art. For example, one of the filters concentrates the energy and the other acts on the result of the convolution between the channel and the concentration filter in order to make the channel as close as possible to an ideal pulse response.
Other techniques have been developed as variants of these techniques, in particular, the min-ISI technique can be cited, developed in the document “Equalization for discrete multitone receivers to maximize bit rate” (Arslan, B. L. Evans, and S. Kiaei, IEEE Trans. Signal Processing, vol. 49, no. 12, pp. 3123-3135, 2001), which aims to be free of the interferences in the frequency domain and consists in generalising the MSSNR technique previously described.
The inventors have found that these techniques are however limited by two major drawbacks: firstly the complexity of the calculations of the coefficients of the reduction filter or filters and secondly the fact that these techniques do not prove to be sufficiently effective on certain types of channel, such as ultra wide band channels.